Abstract
It is shown that for each positive integer n, there exists a nondiscrete Hausdorff topological group of cardinality ℵ n with no proper subgroup of the same cardinality and with each proper subgroup discrete. This result is typical of those proved here using a method introduced by A.Yu. Ol'shanskii. It is also shown that there exists a continuum of pairwise algebraically nonisomorphic nondiscrete Hausdorff topological groups, each of which contains every finite group of odd order and has all of its proper subgroups finite.
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